Question: Multiply the following complex numbers, marked as blue dots on the graph: $(3 e^{11\pi i / 12}) \cdot (3 e^{\pi i / 3})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $3 e^{11\pi i / 12}$ ) has angle $\frac{11}{12}\pi$ and radius $3$ The second number ( $3 e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius $3$ The radius of the result will be $3 \cdot 3$ , which is $9$ The angle of the result is $\frac{11}{12}\pi + \frac{1}{3}\pi = \frac{5}{4}\pi$ The radius of the result is $9$ and the angle of the result is $\frac{5}{4}\pi$.